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Joint Trajectory and Resource Allocation Design for Energy-Efficient Secure UAV Communication Systems

Yuanxin Cai, Zhiqiang Wei, Ruide Li, Derrick Wing Kwan Ng, Jinhong Yuan

arXiv:2003.07028v1cs.ITeess.SP

TL;DR

The paper addresses joint trajectory, resource-allocation, and jamming design for energy-efficient secure UAV-OFDMA communication with multiple users and uncertain eavesdroppers. It decomposes the non-convex problem into alternating subproblems solved with successive convex approximation and Dinkelbach’s method, obtaining a low-complexity suboptimal algorithm. Simulations show fast convergence and that multi-antenna jamming improves trajectory flexibility, energy efficiency, and security.

  • Problem

    Secure UAV communication must jointly address energy efficiency, multiple users, QoS, security constraints, and imperfect eavesdropper information.

  • Method

    The paper jointly designs the information UAV trajectory, resource allocation, and jammer policy through alternating optimization using SCA and Dinkelbach’s method.

  • Results

    Simulations show convergence within a small number of iterations and demonstrate benefits from multi-antenna jamming for energy efficiency, trajectory flexibility, and secure communication.

  • Takeaways & Limitations

    A multi-antenna jammer UAV can focus artificial noise on eavesdroppers and provide greater flexibility in designing the information UAV trajectory.

  • Takeaways & Limitations

    The jammer UAV is assumed to follow a fixed trajectory with constant velocity; optimizing its trajectory is left for future work.

Abstract

from arXiv · show

In this paper, we study the trajectory and resource allocation design for downlink energy-efficient secure unmanned aerial vehicle (UAV) communication systems, where an information UAV assisted by a multi-antenna jammer UAV serves multiple ground users in the existence of multiple ground eavesdroppers. The resource allocation strategy and the trajectory of the information UAV, and the jamming policy of the jammer UAV are jointly optimized for maximizing the system energy efficiency. The joint design is formulated as a non-convex optimization problem taking into account the quality of service (QoS) requirement, the security constraint, and the imperfect channel state information (CSI) of the eavesdroppers. The formulated problem is generally intractable. As a compromise approach, the problem is divided into two subproblems which facilitates the design of a low-complexity suboptimal algorithm based on alternating optimization approach. Simulation results illustrate that the proposed algorithm converges within a small number of iterations and demonstrate some interesting insights: (1) the introduction of a jammer UAV facilitates a highly flexible trajectory design of the information UAV which is critical to improving the system energy efficiency; (2) by exploiting the spatial degrees of freedom brought by the multi-antenna jammer UAV, our proposed design can focus the artificial noise on eavesdroppers offering a strong security mean to the system.

I. INTRODUCTION

The paper motivates secure, energy-efficient UAV communication by combining UAV mobility with a multi-antenna jammer under multiple-user, uncertain-eavesdropper conditions. It formulates a joint non-convex design and develops an alternating suboptimal solution.

  • Motivation: UAV mobility can improve communication performance through proximity and strong line-of-sight channels, but onboard energy limitations make trajectory and power consumption important design concerns.Flight power depends on trajectory and velocity, while prior work did not jointly address all relevant energy components and communication resource allocation.
  • Motivation: LoS-dominated UAV channels are vulnerable to eavesdropping, while prior secure designs were limited by single-user settings, known eavesdropper locations, or unestablished energy efficiency.The paper targets multiple users and imperfect eavesdropper information.
  • System and design: The joint design maximizes energy efficiency subject to user-rate, eavesdropper-leakage, and other system constraints, while accounting for imperfect eavesdropper location information.The jammer follows a fixed trajectory and constant velocity, whereas the information UAV trajectory and resource allocation are jointly designed.
  • Solution approach: The non-convex problem is divided into two subproblems solved alternatively using successive convex approximation and Dinkelbach’s method.The resulting algorithm is suboptimal and has polynomial-time computational complexity.
  • System and design: The system contains an information UAV, multiple single-antenna users and eavesdroppers, and a multi-antenna jammer UAV with NJ > E antennas.The jammer generates artificial noise to combat potential eavesdroppers.

C. UAV Power Consumption Model

The power-consumption model combines UAV flight power, communication power, scheduling, and beamformed jamming under a fixed jammer trajectory. The channel model uses LoS propagation and multi-antenna steering toward users and eavesdroppers.

  • Flight power: The information and jammer UAV flight-power models depend on their flight velocities, with the jammer using a fixed path and a selected constant velocity.The flight-power function is convex with respect to flight velocity for both UAVs.
  • Communication power: Information transmit power, amplifier inefficiency, circuit power, and subcarrier assignment contribute to total system power consumption.The binary assignment variable αI_k,i[n] indicates whether subcarrier i is assigned to user k at time slot n.
  • Artificial-noise jamming: The jammer’s multi-antenna artificial noise can be beamformed toward eavesdroppers while also creating interference at legitimate users.The jammer’s spatial degrees of freedom support deliberate eavesdropper-channel interference, and transmission can be set to zero when jamming does not improve performance.
  • Downlink channels: The channel model assumes LoS-dominated links and uses vertical and horizontal angles of departure to characterize jammer-array channels.The jammer-array geometry includes antenna separation and NJx × NJy array dimensions.
  • Downlink channels: Eavesdropper location uncertainty is represented through an uncertain region around each estimated location and incorporated into the jammer-channel model.The paper adopts a worst-case uncertainty model rather than a probabilistic model.

III. RESOURCE ALLOCATION AND TRAJECTORY DESIGN

The design uses achievable user rates, eavesdropper leakage rates, energy efficiency, scheduling, power allocation, artificial-noise covariance, and information-UAV trajectory variables. Both flight and communication power matter for energy efficiency and security.

  • Performance metrics: User achievable rate is computed from subcarrier bandwidth, scheduling, and the user’s received SINR at each time slot.The rate expression uses RU_k,i[n] = WαI_k,i[n] log2(1 + ΓIU_k,i[n]).
  • Performance metrics: Information leakage to each eavesdropper is characterized by its received SINR on each user-subcarrier-time combination.The jammer’s artificial noise interferes with both legitimate-user and eavesdropper channels.
  • Performance metrics: System energy efficiency is defined in bits per Joule using the aggregate achievable communication rate and system power consumption.The optimization includes user scheduling, information transmit powers, and artificial-noise covariance matrices.
  • Joint design: The formulation jointly optimizes communication variables and the information UAV trajectory while accounting for flight and communication power consumption.The paper emphasizes that optimizing both power components is important for energy efficiency and communication security.

B. Optimization Problem Formulation

The paper formulates energy-efficient secure UAV-OFDMA design as a constrained optimization over scheduling, power, artificial noise, information-UAV trajectory, and velocity. The formulation includes QoS, leakage, motion, power, and safety requirements, while auxiliary reformulations address non-convex couplings.

  • B. Optimization Problem Formulation: The objective maximizes system energy efficiency over user scheduling, transmit power, artificial noise, information-UAV trajectory, and flight velocity.
  • B. Optimization Problem Formulation: The formulation can be extended to three-dimensional aviation, although the presented constraint description uses the stated model.
  • B. Optimization Problem Formulation: The model includes user scheduling, nonnegative and peak transmit-power, total-power-budget, data-rate, eavesdropper-leakage, motion, and collision-avoidance constraints.The leakage constraint accounts for eavesdropper location uncertainty, while trajectory constraints specify initial conditions, velocity, acceleration, and minimum UAV separation.
  • IV. PROBLEM SOLUTION: The resulting problem is non-convex and generally computationally intractable for globally optimal solution by brute force, motivating an efficient suboptimal design.
  • IV. PROBLEM SOLUTION: Introducing the information-UAV flight velocity as an explicit variable simplifies the resource-allocation formulation by avoiding a more complicated trajectory-only flight-power expression.
  • IV. PROBLEM SOLUTION: The problem is divided into two alternating subproblems: resource allocation and artificial-noise optimization for fixed trajectory, followed by trajectory and velocity optimization for fixed resources.
  • A. Sub-problem 1: Optimizing User Scheduling, Communication Transmit Power Allocation, and Artificial Noise: In sub-problem 1, non-convex couplings involving scheduling and power variables are addressed using auxiliary variables and an equivalent big-M reformulation.

C18 : ˜ZJ

The first subproblem handles scheduling, communication power, and artificial noise for a fixed information-UAV trajectory and velocity. Successive convex approximation and fractional programming produce iterative convex subproblems, with rank-one artificial-noise structure under feasibility.

  • C18 : ˜ZJ: Binary user scheduling is rewritten equivalently, and its continuous time-sharing representation is handled through a penalty factor χ ≫1.The scheduling variable αI_k,i[n] serves as a time-sharing factor, while χ penalizes fractional values that are not 0 or 1.
  • C18 : ˜ZJ: The non-convex data-rate terms are lower-bounded using first-order Taylor expansions within successive convex approximation.
  • C18 : ˜ZJ: A safe approximation imposes a stricter leakage-SINR constraint, so the resulting solution provides a performance lower bound for the original problem.
  • C18 : ˜ZJ: Dinkelbach’s method transforms the fractional energy-efficiency objective into a subtractive form and repeatedly solves a convex optimization problem.
  • C18 : ˜ZJ: If the convex subproblem is feasible, the optimal artificial-noise matrix satisfies Rank(Z) ≤1, making rank-one beamforming optimal despite multiple eavesdroppers.

B. Sub-problem 2: Optimizing Information UAV’s Trajectory and Flight Velocity

The second subproblem optimizes the information UAV’s trajectory and flight velocity while preserving resource and security constraints. Slack variables, S-Procedure transformations, SCA, and Dinkelbach iterations yield a convex subproblem at each iteration.

  • B. Sub-problem 2: Optimizing Information UAV’s Trajectory and Flight Velocity: For fixed scheduling, transmit-power allocation, and artificial noise, the second subproblem optimizes the information UAV’s trajectory and flight velocity.
  • B. Sub-problem 2: Optimizing Information UAV’s Trajectory and Flight Velocity: Slack variables transform the non-convex trajectory formulation into an equivalent form whose relevant flight-power expressions are convex for positive slack values.
  • B. Sub-problem 2: Optimizing Information UAV’s Trajectory and Flight Velocity: Eavesdropper location uncertainty creates infinitely many leakage constraints, which the S-Procedure converts into a finite set of linear matrix inequalities.
  • B. Sub-problem 2: Optimizing Information UAV’s Trajectory and Flight Velocity: Successive convex approximation uses first-order Taylor bounds for data-rate, distance, and velocity-related terms to construct tractable trajectory updates.
  • B. Sub-problem 2: Optimizing Information UAV’s Trajectory and Flight Velocity: The objective’s numerator and denominator are replaced by equivalent or lower-bound forms, producing a suboptimal optimization problem for trajectory and velocity updates.
  • B. Sub-problem 2: Optimizing Information UAV’s Trajectory and Flight Velocity: The overall procedure alternates Algorithm 1 for resource allocation with Algorithm 3 for trajectory and velocity optimization.
  • B. Sub-problem 2: Optimizing Information UAV’s Trajectory and Flight Velocity: Dinkelbach’s method solves the resulting convex formulation iteratively, using numerical convex-programming solvers such as CVX.

C. Overall Algorithm

The overall algorithm alternates the two subproblem solvers while preserving feasibility and non-decreasing objective value. The resulting method converges to a suboptimal solution with polynomial-time computational complexity.

  • C. Overall Algorithm: The overall algorithm repeatedly applies the resource-allocation and trajectory-optimization subproblem solvers.
  • C. Overall Algorithm: Because the feasible set is compact and the objective value is non-decreasing across alternating updates, convergence of the proposed algorithm is guaranteed.
  • C. Overall Algorithm: Table II lists the simulation parameters used to evaluate the proposed algorithms.
  • C. Overall Algorithm: The use of SCA and the S-Procedure yields convergence to a suboptimal solution of the original optimization problem.
  • C. Overall Algorithm: The proposed suboptimal algorithm has polynomial-time computational complexity, with complexity dominated by semidefinite programming for sub-problem 1.

V. NUMERICAL RESULTS

The numerical evaluation compares the proposed algorithm with three baseline schemes for system energy efficiency. The baselines vary jammer availability, jammer antennas, and the information UAV’s trajectory.

  • The proposed algorithm, “PA,” is evaluated against three baseline schemes for system energy efficiency.The baselines include No jammer UAV, Single-antenna jammer UAV, and Straight locus information UAV.
  • The “NJ” baseline removes the jammer UAV and obtains resource allocation and trajectory using a similar approach to prior work.
  • The “SLI” baseline fixes the information UAV to a constant-speed straight trajectory while retaining the jammer UAV setting of “PA”.Its resource allocation is optimized with the information UAV’s trajectory fixed.

A. Convergence of the Proposed Algorithm and Baseline Schemes

The proposed alternating-optimization scheme is evaluated for mission durations of 50, 25, and 13 seconds. Figure 4 examines how system energy efficiency evolves with the iteration count.

  • Figure 4 evaluates convergence for mission durations T = 50 s, T = 25 s, and T = 13 s.These settings correspond to N = 500, N = 200, and N = 130 time slots, respectively.
  • The jammer UAV orbits around the center of the eavesdroppers areas in the evaluated configurations.
  • For each mission duration, the proposed scheme’s system energy efficiency converges to a corresponding value as iterations proceed.

B. Impact of Number of Users

System energy efficiency first benefits from increasing the number of users through multiuser diversity, then declines as minimum-rate constraints restrict resource allocation flexibility. The proposed algorithm remains better than the baseline schemes as user count increases.

  • With K = 2 users, all schemes achieve much higher energy efficiency than with K = 1.The simulation sets each user’s minimum data-rate requirement to Rmin = 1 Mbits/s.
  • When K exceeds 2, minimum data-rate constraints become stringent and reduce resource-allocation flexibility, lowering system energy efficiency.
  • The “PA” scheme consistently outperforms the other baseline schemes as the number of users increases.

C. Impact of Jammer UAV’s Trajectory

The jammer UAV’s trajectory and antenna configuration shape how the information UAV allocates movement, communication power, and artificial noise, affecting secure energy efficiency. Flexible trajectories and focused jamming help manage leakage while preserving efficient communication.

  • C. Impact of Jammer UAV’s Trajectory: A jammer path cruising among all eavesdroppers gives the information UAV a more favorable trajectory than several fixed circular alternatives.The compared jammer trajectories include CSA, CEA, and paths centered at estimated eavesdropper locations.
  • D. Trajectories of Information UAV: At T = 50 s, the information UAV varies speed and hovers above user 2, while avoiding hovering above user 1 because user 1 is closer to an eavesdropper.Communication power is allocated first to user 1 and later to user 2.
  • D. Trajectories of Information UAV: During high-leakage slots, the jammer uses full-power focused artificial noise while the information UAV reduces transmit power to protect communication security.Multiple jammer antennas steer a sharp noise beam that can impair both eavesdroppers efficiently.
  • D. Trajectories of Information UAV: The information UAV’s trajectory is extremely important for achieving high system energy efficiency and secure communication.The associated communication-power and jamming patterns remain similar across mission durations.
  • E. Energy Efficiency: Energy efficiency increases with jammer antennas but becomes saturated when antenna circuit power outweighs additional spatial-flexibility gains.The simulation sets each jammer antenna’s circuit power consumption to PCJ = 0.1 Watt.
  • E. Energy Efficiency: At low-to-moderate communication peak power, energy efficiency rises, then saturates as the information UAV clips transmit power at its optimal value.With fixed artificial-noise peak power, larger communication peak power also makes the security constraint more stringent.

VII. APPENDIX PROOF OF THEOREM 1

The proof establishes convexity and applies Lagrangian and KKT conditions to characterize the optimal energy matrix ZJ when the jammer UAV’s trajectory is fixed.

  • Convexity and KKT analysis: The optimization problem (42) is jointly convex in its optimization variables and satisfies Slater’s constraint qualification.This permits the Lagrangian-based proof approach.
  • Convexity and KKT analysis: The proof derives the Lagrangian of (42), with matrix and scalar multipliers associated with the stated constraints.Yi,n, Xi,n, and Vi,n are positive-semidefinite Lagrange multiplier matrices; µ, ν, and ϑ are scalar multiplier collections.
  • Optimal energy-matrix structure: For fixed jammer UAV trajectory, the KKT conditions and complementary slackness constrain the columns of ZJ∗[n] to the null space of Yi,n∗.This null-space condition is used to reveal the structure of the optimal energy matrix.
  • Optimal energy-matrix structure: The energy-efficiency value of the system is positive, supporting the resulting solution for ZJ.The proof explicitly uses positivity of the energy-efficiency value in deriving the solution.
  • Optimal energy-matrix structure: The relevant null space is spanned by the unit-norm eigenvector associated with the maximum eigenvalue λmax of the matrix Ω.The proof uses this eigenstructure to obtain the optimal energy-matrix structure and a bounded optimal dual solution.
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